Condition numbers for linear systems and Kronecker product linear systems with multiple right-hand sides

Authors:
Haiming Zhang;Hua Xiang;Yimin Wei
Affiliations:
Institute of Mathematics, Fudan University, Shanghai, P.R. China;School of Mathematics and Statistics, Wuhan University, Wuhan, P.R. China;School of Mathematical Sciences, Fudan University, Shanghai, P.R. China,Ministry of Education, Key Laboratory of Mathematics for Nonlinear Sciences (Fudan University), P.R. China
Venue:
International Journal of Computer Mathematics
Year:
2007

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Abstract

In this paper we investigate linear systems with multiple right-handed sides in the form of AX=B and (A ⊗ B)X=C. We derive normwise, mixed and componentwise condition numbers for these linear systems. Examples are given to evaluate the tightness of the first-order perturbation bounds.